The answer probably depends on what your utility is nearest to being proportional to the logarithm of.
Most likely your utility (so far as you have one) looks like other_stuff + f(wealth) where wealth = g(annual_income, liquid_assets, other_assets) or something of the kind, where f and g are functions about which we don’t know very much. It’s probably OK to assume that g is just a linear combination of its inputs. So it seems like there are two things to do.
Figure out what g looks like by imagining various possible states-of-wealth and ordering them by preference. E.g., would you rather an income of £50k/year and assets of £500k of which £100k are easily accessible, or an income of £200k/year and no assets, or no income and assets of £1M of which £200k are easily accessible? Etc.
Figure out what f looks like by imagining various gambles. E.g., suppose you have no assets; would you prefer a salary of £30k or of (£25k or £40k, equiprobably)?
And then you can try plugging the result into the Kelly formula, seeing how over-risky it feels, and (if you are so inclined) correcting for excess risk aversion not already factored into f.
The answer probably depends on what your utility is nearest to being proportional to the logarithm of.
Most likely your utility (so far as you have one) looks like other_stuff + f(wealth) where wealth = g(annual_income, liquid_assets, other_assets) or something of the kind, where f and g are functions about which we don’t know very much. It’s probably OK to assume that g is just a linear combination of its inputs. So it seems like there are two things to do.
Figure out what g looks like by imagining various possible states-of-wealth and ordering them by preference. E.g., would you rather an income of £50k/year and assets of £500k of which £100k are easily accessible, or an income of £200k/year and no assets, or no income and assets of £1M of which £200k are easily accessible? Etc.
Figure out what f looks like by imagining various gambles. E.g., suppose you have no assets; would you prefer a salary of £30k or of (£25k or £40k, equiprobably)?
And then you can try plugging the result into the Kelly formula, seeing how over-risky it feels, and (if you are so inclined) correcting for excess risk aversion not already factored into f.